Saw chains for wood chainsaws include cutter links having sharp cutting elements for cutting through wood. The cutting elements may become dull from repeated use. Accordingly, the cutting elements may be periodically sharpened to extend the life of the saw chain. In some cases, the cutting element may be sharpened by bringing a sharpening stone into contact with the cutting element while the cutter link traverses a guide bar of the chainsaw. Some saw chains further include one or more dresser links (also referred to as conditioning links) having a region with a conditioning material to condition the sharpening stone in order to compensate for grooves that may be formed by the cutting element and/or other chain elements. These saw chains may include left and right dresser links that oppose one another on the saw chain. However, the left and right dresser links may leave and/or form a groove in the middle of the sharpening stone.